1
AIEEE 2005
+4
-1
Out of Syllabus
If the angel $$\theta$$ between the line $${{x + 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 2}$$ and

the plane $$2x - y + \sqrt \lambda \,\,z + 4 = 0$$ is such that $$\sin \,\,\theta = {1 \over 3}$$ then value of $$\lambda$$ is :
A
$${5 \over 3}$$
B
$${-3 \over 5}$$
C
$${3 \over 4}$$
D
$${-4 \over 3}$$
2
AIEEE 2005
+4
-1
Out of Syllabus
The distance between the line

$$\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),$$ and the plane

$$\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5$$ is
A
$${{10} \over 9}$$
B
$${{10} \over {3\sqrt 3 }}$$
C
$${{3} \over 10}$$
D
$${{10} \over 3}$$
3
AIEEE 2005
+4
-1
The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :
A
$${0^ \circ }$$
B
$${90^ \circ }$$
C
$${45^ \circ }$$
D
$${30^ \circ }$$
4
AIEEE 2005
+4
-1
Out of Syllabus
If the plane $$2ax-3ay+4az+6=0$$ passes through the midpoint of the line joining the centres of the spheres

$${x^2} + {y^2} + {z^2} + 6x - 8y - 2z = 13$$ and

$${x^2} + {y^2} + {z^2} - 10x + 4y - 2z = 8$$ then a equals :
A
$$-1$$
B
$$1$$
C
$$-2$$
D
$$2$$
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